In fact, only the first two of these forms appear in his surviving works and the third
was written by a later scholar. William used the principle to justify many
conclusions, including the statement that "God's existence cannot be deduced by reason
alone." That one didn't make him very popular with the Pope.

Many scientists have adopted or reinvented Occam's Razor, as in Leibniz's "identity of
observables" and Isaac Newton stated the rule: "We are to admit no more causes of
natural things than such as are both true and sufficient to explain their
appearances."

The most useful statement of the principle for scientists is
"when you have two competing theories that make exactly the same predictions, the
simpler one is the better."

In physics we use the razor to shave away metaphysical concepts. The canonical
example is Einstein's theory of special relativity compared with Lorentz's theory that
ruler's contract and clocks slow down when in motion through the ether. Einstein's
equations for transforming spacetime are the same as Lorentz's equations for transforming
rulers and clocks, but Einstein and Poincaré recognised that the ether could not be
detected according to the equations of Lorentz and Maxwell. By Occam's razor it had
to be eliminated.

The principle has also been used to justify uncertainty in quantum mechanics.
Heisenberg deduced his uncertainty principle from the quantum nature of light and the
effect of measurement.

Stephen Hawking writes in A Brief History of Time:
"We could still imagine that there is a set of laws that determines events completely
for some supernatural being, who could observe the present state of the universe without
disturbing it. However, such models of the universe are not of much interest to us
mortals. It seems better to employ the principle known as Occam's razor and cut out
all the features of the theory that cannot be observed."

But uncertainty and the non-existence of the ether cannot be deduced from Occam's Razor
alone. It can separate two theories that make the same predictions, but does not
rule out other theories that might make a different prediction. Empirical evidence
is also required, and Occam himself argued for empiricism, not against
it.

Ernst Mach advocated a version of Occam's razor which he called the Principle of
Economy, stating that "Scientists must use the simplest means of arriving at their
results and exclude everything not perceived by the senses." Taken to its
logical conclusion, this philosophy becomes positivism; the belief that there is
no difference between something that exists but is not observable and something that
doesn't exist at all. Mach influenced Einstein when he argued that space and time
are not absolute but he also applied positivism to molecules. Mach and his followers
claimed that molecules were metaphysical because they were too small to detect
directly. This was despite the success the molecular theory had in explaining
chemical reactions and thermodynamics. It is ironic that while applying the
principle of economy to throw out the concept of the ether and an absolute rest frame,
Einstein published almost simultaneously a paper on brownian motion which confirmed the
reality of molecules and thus dealt a blow against the use of positivism. The moral
of this story is that Occam's razor should not be wielded blindly. As Einstein put
it in his Autobiographical notes:

"This is an interesting example of the fact that even scholars of audacious spirit and
fine instinct can be obstructed in the interpretation of facts by philosophical
prejudices."

Occam's razor is often cited in stronger forms than Occam intended, as in the
following statements. . .

"If you have two theories that both explain the observed facts, then you should use
the simplest until more evidence comes along"

"The simplest explanation for some phenomenon is more likely to be accurate than
more complicated explanations."

"If you have two equally likely solutions to a problem, choose the simplest."

"The explanation requiring the fewest assumptions is most likely to be correct."

. . .or in the only form that takes its own advice. . .
"Keep things simple!"

Notice how the principle has strengthened in these forms which should be more
correctly called the law of parsimony, or the rule of simplicity.
To begin with, we used Occam's razor to separate theories that would predict the same
result for all experiments. Now we are trying to choose between theories that make
different predictions. This is not what Occam intended. Should we not test
those predictions instead? Obviously we should eventually, but suppose we are at an
early stage and are not yet ready to do the experiments. We are just looking for
guidance in developing a theory.

This principle goes back at least as far as Aristotle, who wrote "Nature operates in
the shortest way possible." Aristotle went too far in believing that experiment
and observation were unnecessary. The principle of simplicity works as a heuristic
rule of thumb, but some people quote it as if it were an axiom of physics, which it is
not. It can work well in philosophy or particle physics, but less often so in
cosmology or psychology, where things usually turn out to be more complicated than you
ever expected. Perhaps a quote from Shakespeare would be more appropriate than
Occam's razor: "There are more things in heaven and earth, Horatio, than are dreamt of
in your philosophy.".

Simplicity is subjective and the universe does not always have the same ideas about
simplicity as we do. Successful theorists often speak of symmetry and beauty as well
as simplicity. In 1939 Paul Dirac wrote "The research worker, in his effort to
express the fundamental laws of Nature in mathematical form, should strive mainly for
mathematical beauty. It often happens that the requirements of simplicity and beauty
are the same, but where they clash the latter must take precedence."

The law of parsimony is no substitute for insight, logic and the scientific
method. It should never be relied upon to make or defend a conclusion. As
arbiters of correctness, only logical consistency and empirical evidence are
absolute. Dirac was very successful with his method. He constructed the
relativistic field equation for the electron and used it to predict the positron.
But he was not suggesting that physics should be based on mathematical beauty alone.
He fully appreciated the need for experimental verification.

The final word is of unknown origin, although it's often attributed to Einstein,
himself a master of the quotable one liner:

"Everything should be made as simple as possible, but not simpler."

The pithiness of this quote disguises the fact that no one knows whether Einstein
actually said it (this version comes from the Reader's Digest, 1977 [US: July, UK:
October?). It may well be a precis of the last few pages of his "The Meaning of
Relativity" (5th edition), in which he writes of his unified field theory: "In my
opinion the theory here is the logically simplest relativistic field theory that is at all
possible. But this does not mean that Nature might not obey a more complex
theory. More complex theories have frequently been proposed. . . In my view,
such more complicated systems and their combinations should be considered only if there
exist physical-empirical reasons to do so."